This is a weekend after the big and full ‘Strawberry Moon’. We have seen how things can look different depending on where we stand. I am giving 2 examples of math quizzes that may move you to another position and let you see math in different lights.
Example 1 (from Jeff Suzuki a mathematician and historian of mathematics, posted on https://www.quora.com/Can-you-use-algebra-to-solve-most-calculus-problems-if-not-all ")
Find the point X that minimizes the total distance AX + XB:
This is a standard calculus 1 optimization problem.
The geometric solution is so insanely simple that I won’t even solve it; I’ll draw the diagram and you’ll know what the solution is. Here, I’ve reflected B across the line to B’.
[The answer 'geometrically' is of course the straight line between 2 points is the shortest (minimum). To calculate the answer, we would need 'data' such as the distance between points A and B, the height of A, the height of B,..
Now let me ask a question: "What are the minimum data, we need to give the answer to this problem?]
Example 2 (from Tony Wang a bronze medalist International Math Olympiads (IMO) 2018 in his post https://www.quora.com/What-are-some-math-problems-that-appear-to-require-calculus-but-only-need-algebra-geometry-to-solve . He tells how to fit math problems into new context and how that allows quick and easy solutions.)
Find the total distance a ray (the black line) travels from A to B.
By mirroring figure 1, first along the CD edge to add CDB'A' rectangle, then by mirroring along A'D edge to produce figure 2, we can see how Tony Wang change a ray's multiple deflections into a straight ray tracing problem. The solution is now just a simple application of Pythagoras theorem.
[The solution (shown as the yellow line) is quite simple to calculate.]
As we can see how these quizzes are easily solved in new frames of thinking. Many much more difficult math problems are by shifting viewpoints. Alexander Grothendieck (28 March1928 - 13 November 2014) was a mathematician and pioneer of modern algebraic geometry who showed the way to look at very difficult math problems in different ways and let the solutions flow out ('mathematically'/naturally) as consequences.
Have a happy week and share your happy face;-)
The Timeline Episode 1 ผงชูรส : ตำนานความนัวแห่งเอเชียบูรพา
ผงชูรส ตำนานความนัวแห่งเอเชียบูรพา ผงชูรส ตำรับความนัวที่มีติดไว้ทุกครัวเรือน ใครจะไปรู้ว่าผลึกแท่งสี่เหลี่ยมยาวๆนี้ จะเพิ่มความกลมกล่อมให้มื้ออาหารของเราได้อย่างมหัศจรรย์ วันนี้เราจะพาทุกคนย้อนเวลาไปดูกันว่าความนัวนี้มีที่มาที่ไปอย่างไรกับ อัตนัย The Timeline (เมื่อเวลา…เล่าเรื่อง)
ฟังตำนานผงชูรสได้ที่: https://www.attanai.com/video/thetimeline/revolution-monosodium-glutamate/